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  2. Meshfree methods - Wikipedia

    en.wikipedia.org/wiki/Meshfree_methods

    Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field .

  3. Embarrassingly parallel - Wikipedia

    en.wikipedia.org/wiki/Embarrassingly_parallel

    The opposite of embarrassingly parallel problems are inherently serial problems, which cannot be parallelized at all. A common example of an embarrassingly parallel problem is 3D video rendering handled by a graphics processing unit, where each frame (forward method) or pixel (ray tracing method) can be handled with no interdependency. [3]

  4. Overdetermined system - Wikipedia

    en.wikipedia.org/wiki/Overdetermined_system

    For the system =, the least squares formula is obtained from the problem ‖ ‖, the solution of which can be written with the normal equations, [3] = (), where indicates a matrix transpose, provided exists (that is, provided A has full column rank). With this formula an approximate solution is found when no exact solution exists, and it gives ...

  5. Numerical analysis - Wikipedia

    en.wikipedia.org/wiki/Numerical_analysis

    The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.

  6. Comparison of optimization software - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_optimization...

    Given a system transforming a set of inputs to output values, described by a mathematical function f, optimization refers to the generation and selection of the best solution from some set of available alternatives, [1] by systematically choosing input values from within an allowed set, computing the value of the function, and recording the best value found during the process.

  7. Solver - Wikipedia

    en.wikipedia.org/wiki/Solver

    The General Problem Solver (GPS) is a particular computer program created in 1957 by Herbert Simon, J. C. Shaw, and Allen Newell intended to work as a universal problem solver, that theoretically can be used to solve every possible problem that can be formalized in a symbolic system, given the right input configuration.

  8. Nonlinear system - Wikipedia

    en.wikipedia.org/wiki/Nonlinear_system

    In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]

  9. MUSCL scheme - Wikipedia

    en.wikipedia.org/wiki/MUSCL_scheme

    The diagram opposite shows a 3rd order solution to G A Sod's shock tube problem (Sod, 1978) using the above high resolution Kurganov and Tadmor Central Scheme (KT) but with parabolic reconstruction and van Albada limiter. This again illustrates the effectiveness of the MUSCL approach to solving the Euler equations.